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math.MG2004★ 27 cited
The max-plus Martin boundary
Marianne Akian, Stephane Gaubert, Cormac Walsh
We develop an idempotent version of probabilistic potential theory. The goal is to describe the set of max-plus harmonic functions, which give the stationary solutions of determini…
math.MG2004★ 8 cited
A Metric Inequality for the Thompson and Hilbert Geometries
Cormac Walsh, Roger D. Nussbaum
There are two natural metrics defined on an arbitrary convex cone: Thompson's part metric and Hilbert's projective metric. For both, we establish an inequality giving information a…